Bush having tip of spine inside to pierce (5)
I believe the answer is:
gorse
'bush' is the definition.
(gorse is a kind of bush)
'tip of spine inside to pierce' is the wordplay.
'tip of' says to take the initial letters.
'inside' means one lot of letters goes inside another.
'to pierce' becomes 'gore' (goring is a kind of piercing).
The first letter of 'spine' is 's'.
's' put inside 'gore' is 'GORSE'.
'having' acts as a link.
(Other definitions for gorse that I've seen before include "Moorland shrub" , "Prickly heath shrub" , "Prickly moorland plant" , "Wild shrub with yellow flowers and sharp thorns, common on hillsides" , "Yellow-flowering shrub" .)